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problem08_83

# University Physics with Modern Physics with Mastering Physics (11th Edition)

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8.83: a) In terms of the primed coordinates, , 2 2 ) ( ) ( cm 2 cm 2 cm cm cm cm cm 2 v v v v v v v v v v + + = + + = + + = A A A A A A A A v v v v v with a similar expression for . 2 B v The total kinetic energy is then ( 29 ( 29 ( 29 [ ] . . . 2 2 1 ) ( 2 1 2 2 1 2 2 1 2 1 2 1 cm cm 2 2 2 cm cm 2 cm 2 cm 2 cm 2 2 2 v m v m m m v m m v v m v v m v m v m K B B A A B B A A B A B B B A A A B B A A v v v v v v v v + + + + + = + + + + + = + = The last term in brackets can be expressed as , ) ( 2 cm v v v + B B A A m m and the term cm ) m ( v v v v v B A B B A A B B A A m m m m m + - + = + , 0 = and so the term in square brackets in the expression for the kinetic energy vanishes,
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Unformatted text preview: showing the desired result. b) In any collision for which other forces may be neglected the velocity of the center of mass does not change, and the 2 cm 2 1 Mv in the kinetic energy will not change. The other terms can be zero (for a perfectly inelastic collision, which is not likely), but never negative, so the minimum possible kinetic energy is . 2 cm 2 1 Mv...
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